In coherent nonlinear spectroscopy, the sample is probed by measuring processes of energy exchange between photons interacting with the sample. One of the most common nonlinear spectroscopy methods is coherent anti-stokes Raman scattering (CARS), a coherent four-wave mixing process involving the generation of a coherent vibration in the probed medium. In CARS, three laser photons, a pump photon (ωp) a probe photon (ωpr) and the Stokes photon (ωs), overlap in the medium under investigation. By nonlinear interaction with the molecules a fourth coherent photon (ωAS) with the anti-Stokes frequency ωAS=ωp−ωs+ωpr is generated.
The CARS process can be visualized in a molecular energy level diagram as depicted in FIG. 1, where |i and |β are molecular rovibrational states, and |α and |β are virtual levels. Resonant enhancement of the CARS process occurs when the frequency difference ΩR=ωp−ωs coincides with a vibrational level of the medium.
The CARS process, as a coherent scattering process, has to fulfill a phase matching condition, which is equivalent to momentum conservation of the photons involved. With the wave vectors of the pump photon (kP), the probe photon (kpr) and the Stokes photon (kS), the wave vector of the Raman signal can be obtained bykAS=kpr+(kP−kS) or kP+kpr=kAS+kS.
In general, there are two conventional different techniques utilizing a multi-beam excitation scheme for measuring a CARS spectrum, as disclosed, for example, in U.S. Pat. Nos. 4,077,719; 4,084,100; 4,405,237; and 4,512,660; and in WO 02/48660.
According to the first technique, the so-called scanning CARS, two narrow bandwidth lasers at ωp and at ωs (having spectral width of the order of the typical linewidth of Raman levels, i.e., 1 cm−1) are tuned over the Raman resonances of the probed species to generate a signal at 2ωp−ωs (in this case ωpr=ωs). The spectral resolution of this technique is mainly determined by the bandwidth of the applied laser sources.
According to the second technique, broadband or multiplex CARS, a broadband Stokes beam (spectral width typical 100-1000 cm−1) can be used to excite several Raman transitions under investigations simultaneously. The use of a narrow band probe and a broadband Stokes beam enables simultaneous measurement of the entire band of the Raman spectrum (see, for example, “Infrared and Raman Spectroscopy,” edited by B. Schrader, VCH, Weinheim, 1995). The spectral resolution of this technique is usually achieved by using a monochromator and a multichannel detection system. Thus, one laser shot is utilized to measure the entire CARS spectrum.
Another possibility to obtain multiplex CARS spectra is to use a time-resolved CARS scheme. In this technique, two relatively broadband exciting pulses are used for simultaneously populating several Raman levels. The spectral data is obtained by measuring the interference pattern of the CARS signal from a third, delayed broadband probe pulse (see, for example, an article of Leonhardt et al., published in Chem. Phys. Lett., 1987, V. 133, P. 373).
Coherent Raman processes have become a valuable tool in the past few decades in femtosecond time-resolved spectroscopy, as well as in combustion studies and condensed-state spectroscopy. For example, Leonhardt et aL describes in Chem. Phys. Lett. 1987, V. 133, P. 373 the measurements of the energy difference and the lifetimes of two (or more) Raman levels by Fourier-decomposing the quantum beats of the CARS signal using femtosecond pulses. This scheme has been recently used to analyze the energy-level diagram of complex molecules.
CARS has recently become a favorable technique for nonlinear depth-resolved microscopy (see, for example, U.S. Pat. No. 6,108,081; WO 02/06778; and scientific articles Zumbusch et al., Phys. Rev. Lett., 1999, V. 82, P. 4142; Hashimoto et al., Opt. Lett., 2000, V. 25, P. 1768; and Volkmer at al., Applied Phys. Lett., 2002, V. 80, P. 1505). CARS microscopy has the potential, for example, for studying live biological specimens while gathering three-dimensional information on their molecular constitution. However, the these CARS microscopes also require two or three narrow-band sources that must be all tightly synchronized and also tunable within the Raman energy range.
It should be appreciated that the signal of CARS (being a result of a nonlinear process) is stronger with short intense pulses. However, the femtosecond CARS techniques suffer from two major difficulties. First, there is an increased strong background signal typically due to the electronic contributions to the third-order susceptibility, both from the sample and from the surrounding medium (i.e., solvent). The second difficulty is associated with a lack of selectivity between neighboring energy levels, due to the large bandwidth of the pulses.
These problems can be solved by coherent quantum control methods. The concept of coherent quantum control of a quantum system is based on the achievement of constructive interference between different quantum paths leading to a desirable outcome, while interfering destructively with paths leading to other outcomes. While schemes of coherent control may involve excitations by continuous waves, most available techniques are also known which involve ultrashort optical pulses. With the recent progress in ultrafast optics, it is now possible to shape ultrashort signals with desired spectral shapes (see, for example, U.S. Pat. No. 6,327,068 assigned to the assignee of the present application).
The inventors of the present invention have recently shown how coherent control techniques can be exploited to improve the CARS spectroscopy employing three femtosecond pulses related to the pump, Stokes and probe beams, respectively. Two approaches have been described for controlling the CARS process. According to the first approach (“Quantum Control of Coherent anti-Stokes Raman Processes” by Oron et al., published in Phys. Rev. A, 2002, V 65, P. 43408), a periodic phase modulation is used to control the population induced by broadband pulses. By shaping both the pump and the Stokes pulses with an appropriate spectral phase function, the nonresonant CARS background has been greatly reduced. This technique also allows for exciting just one out of many vibrational levels, even when all of them are within the spectral bandwidth of the excitation pulses. According to the second approach (“Narrow-Band Coherent Anti-Stokes Raman Signals from Broad-Band Pulses” by Oron et al., published in Phys. Rev. Lett., 2002, V. 88, P. 63004), only the probe pulse is shaped, thereby enabling enhancement of the resolution of the measured CARS spectrum. The achieved spectral resolution becomes significantly better than the bandwidth of the readout pulse. In particular, by tailoring the phase of a 100 femtosecond probe pulse, a narrow-band CARS spectroscopy resonant signal has been obtained with a width of less than 15 cm−1, which is an order of magnitude narrower than the CARS signal from an unshaped, transform limited pulse (all frequency components having the same phase).